MATH 302 week 3 test.docx mostly tested exam questions with well detailed answers

MATH 302 week 3 test.docx mostly tested exam questions with well detailed answers Part 1 of 6 - Binomial Distribution 2.0/ 5.0 Points Question 1 of 20 0.0/ 1.0 Points It is known that 50% of adult workers have ...

MATH 302 week 3 test.docx mostly tested exam questions with well detailed answers Part 1 of 6 - Binomial Distribution 2.0/ 5.0 Points Question 1 of 20 0.0/ 1.0 Points It is known that 50% of adult workers have a high school diploma. If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma? (That is, what is P(X<6) (keep 4 decimal places) Question 2 of 20 1.0/ 1.0 Points Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the P(X ≥ 15) using Excel. Round answer to 4 decimal places. Question 3 of 20 0.0/ 1.0 Points It is known that 20% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the probability that 5 or more of them have a high school diploma? (That is, find P(X≥5) (keep 4 decimal places) Question 4 of 20 1.0/ 1.0 Points If random variable X has a binomial distribution with n =8 and P(success) = p =0.5, find the probability that X is at most 3. (That is, find P(X ≤ 3)) (keep 4 decimal places) Question 5 of 20 0.0/ 1.0 Points If random variable X has a binomial distribution with n=9 and P(success) =p= 0.4, find the standard deviation of X. (keep 4 decimal places) Part 2 of 6 - Contingency Tables 1.0/ 1.0 Points Question 6 of 20 1.0/ 1.0 Points The table shows a random sample of musicians and how they learned to play their instruments. Gender Self-Taught Studied in School Private Instruction Total Female 12 38 22 72 Male 19 24 15 58 Total 31 62 37 130 Find P(musician is a male AND had private instruction). • A. 0.71 • B. 0.12 • C. 0.88 • D. 0.29 Part 3 of 6 - Counting Principle 3.0/ 3.0 Points Question 7 of 20 1.0/ 1.0 Points Find the probability of rolling a sum of two dice that is more than 7. Round answer to 4 decimal places. Question 8 of 20 1.0/ 1.0 Points An experiment is to flip a fair coin three times. What is the probability of getting exactly two heads? Do not round your answer. Question 9 of 20 1.0/ 1.0 Points How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type? Part 4 of 6 – Probability 3.0/ 4.0 Points Question 10 of 20 0.0/ 1.0 Points Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X=x) 0.11 0.06 0.18 0.06 0.59 • A. yes • B. no Question 11 of 20 1.0/ 1.0 Points A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years. 1. Complete Table using the data provided. x P(x) 0 0.12 1 0.18 2 0.30 3 0.15 4 0.10 5 0.10 6 0.05 Question 12 of 20 1.0/ 1.0 Points Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X=x) 0.16 0.11 0.06 - 0.36 0.21 • A. yes • B. no Question 13 of 20 1.0/ 1.0 Points Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 52% 28% 20% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Part 5 of 6 - Poisson Distribution 2.0/ 5.0 Points Question 14 of 20 0.0/ 1.0 Points Suppose a random variable, x, follows a Poisson distribution. Let μ = 2.5 every minute, find the P(X ≥ 125) over an hour. Round answer to 4 decimal places. Answer: 0.9793 Question 15 of 20 1.0/ 1.0 Points Suppose a random variable, x, follows a Poisson distribution. Let μ = 3 every day, find the P(X ≤ 12) over a week. Round answer to 4 decimal places. Answer: 0.0245 Question 16 of 20 0.0/ 1.0 Points If random variable X has a Poisson distribution with mean = 4.5 find the probability that X is more than 4. (That is, find P(X>4) (keep 4 decimal places) Answer: 0.5321 Question 17 of 20 1.0/ 1.0 Points The mean number of visitors at a national park in one weekend is 55. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 71 visitors at this park in one weekend. (That is, find P(X≤71) (keep 4 decimal places) Answer: 0.9841 Question 18 of 20 0.0/ 1.0 Points If random variable X has a Poisson distribution with mean = 10, find the probability that X is more than 8. (That is, find P(X>8) (keep 4 decimal places) Answer: 0.6671 Part 6 of 6 - Probability 2.0/ 2.0 Points Question 19 of 20 1.0/ 1.0 Points A gumball machine contains 350 grape flavored balls, 400 cherry flavored balls, and 550 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine? • A. 0.0347 • B. 0.0482 • C. 0.0350 • D. 0.0531 Question 20 of 20 1.0/ 1.0 Points United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any bloodtype. Their data shows that 43% of people have type O blood and 15% of people have Rh- factor; 52% of people have type O or Rh- factor. Find the probability that a person has both type O blood and the Rh- factor. • A. 94% of people have type O, Rh- blood • B. 6% of people have type O, Rh- blood • C. 33% of people have type O, Rh- blood • D. 5% of people have type O, Rh- blood